Thursday, March 22, 2012

Hyperboloid

Aklego's hyperboloid is another great mathematical kinetic sculpture. A hyperboloid of one sheet is a three dimensional surface defined by the equation (x2/a2)+(y2/b2)-(z2/c2)=1. It essentially looks like a cylinder that's been squeezed in around the waist (I show an image below the video). This is another doubly ruled surface - that is, even though the surface is curved, it is made up of intersecting straight lines (the strings in the picture below). Aklego's video shows how this surface is defined by a straight line sweeping in a circular motion.